Aspects of locally covariant quantum field theory

TL;DR

This thesis explores foundational aspects of locally covariant quantum field theory, including mathematical structures, properties of states, and relations between fields and spacetime, with new proofs and interpretations.

Contribution

It provides new insights into the mathematical and conceptual framework of LCQFT, including modal logic interpretation, properties of Hadamard states, and a representation-independent description of the Dirac field.

Findings

Truncated n-point functions of Hadamard states are smooth for n≠2.

The Dirac field's relations are fully determined by the adjoint, charge conjugation, and Dirac operator.

Relative Cauchy evolution relates to the stress-energy tensor similarly for scalar and Dirac fields.

Abstract

This thesis considers various aspects of locally covariant quantum field theory (LCQFT; see Brunetti et al., Commun.Math.Phys. 237 (2003), 31-68), a mathematical framework to describe axiomatic quantum field theories in curved spacetimes. New results include: a philosophical interpretation of certain aspects of this framework in terms of modal logic; a proof that the truncated n-point functions of any Hadamard state of the free real scalar field are smooth, except for n=2; a description of he free Dirac field in a representation independent way, showing that the theory is determined entirely by the relations between the adjoint map, the charge conjugation map and the Dirac operator; a proof that the relative Cauchy evolution of the free Dirac field is related to its stress-energy-momentum tensor in the same way as for the free real scalar field (cf. loc.cit.); several results on the Reeh-Schlieder property in LCQFT, including but not limited to those of our earlier paper; a new and elegant approach to wave front sets of Banach space-valued distributions, which allows easy proofs and extensions of results in the literature.